Simpson’s Paradox in Canadian Police Clearance Rates

Abstract

Police clearance rates and other forms of aggregated criminal justice data can be susceptible to statistical artefacts such as Simpson’s paradox (Yule-Simpson effect). Simpson’s paradox occurs when a trend apparent in separate data groups reverses itself once the groups are combined. Within 15 years of clearance rate data from the 50 largest Canadian police jurisdictions, 210 instances of Simpson’s paradox were discovered (annual mean = 14.0). These instances included four cases in which a reversal occurred simultaneously in all crime categories and subcategories. This finding suggests the need for caution when using clearance rates as a comparative measure of police performance, particularly between jurisdictions or time periods with different crime mixes. Criminal justice researchers, policy makers, and crime analysts should be aware of Simpson’s paradox and its potential effect on aggregated data. Finally, the possibility of a double reversal must be considered when attempting to resolve Simpson’s paradox.